Stocks opened higher today after the government said hiring picked up in July, but the gains were erased within 25 minutes.

The Dow closed up 61 points, or 0.5 percent, at 11,445. The S&P 500 closed down a point, or 0.1 percent, at 1,199. The Nasdaq composite index closed down 24, or 0.9 percent, at 2,532.

The Dow fell 513 points Thursday, the biggest loss since 2008.

Three stocks fell for every one that rose on the New York Stock Exchange. Trading volume was heavy at 8.6 billion shares.

The hiring report caused the Dow to climb as many as 171 points at the start of trading. Less than 10 minutes after that peak, all the gains had disappeared. Between 10 a.m. and 10:30 a.m., the Dow dipped, rallied, fell, then rose again, only to wind up little changed at the end of the half-hour.

The swings continued all day. The index spent much of the morning and early afternoon down, falling by as many as 243 points. By 1 p.m., it had bounced back and was up 135 points. In late afternoon trading it was up 22 points.

Besides Europe’s growing debt crisis, investors are also concerned about: anemic growth in manufacturing and the service sector and a decline in consumer spending; hiring levels that aren’t high enough to significantly lower the unemployment rate; and the belief that the government is unlikely to stimulate the economy through spending.

European leaders have called emergency meetings to craft a plan that would prevent Italy or Spain from becoming the latest country in the region to require large-scale financial help to avoid a debt default.

The two countries have Europe’s third and fourth largest economies. European leaders and central bankers might not have the cash needed to prop them up until a larger financial rescue fund can be established by a broader group of financial leaders.

“The market got jittery over how the leaders (in the U.S.) reacted to the debt crisis, to how the leaders (in Europe) reacted to the debt crisis,” said Randy Warren, chief investment officer at the investment company Warren Financial Service. “The fear was that they had no plan to deal with the situation.”

Such volatility often follows historic sell-offs like the one that happened Thursday, analysts said. Traders who sold on Thursday are searching for bargain-priced stocks. Those who waited to sell because prices were too low are pocketing profits.

As long as traders disagree about the values of most investments, the market will continue to see-saw, says Daniel Alpert, managing partner at Westwood Capital, a New York investment bank.

“There’s a sense that we’ll see more of the same next week,” Alpert said.

That’s partly because of the shifting signals about whether the European and U.S. government leaders can accelerate a global economic recovery. That uncertainty contributed significantly to the up and down trading on Friday, said Ron Florance, an investment strategist at Wells Fargo Private Bank. Some investors bought stocks after steep price declines, he said. That helped reverse the day’s early losses. Others have rushed to sell their holdings before the weekend, he said.

Florance said he expected stocks to remain volatile for the next several weeks until it’s clear how healthy — or unhealthy — the economy is.

One positive sign: The U.S. economy added 117,000 jobs in July, and hiring in May and June were not as bad as reported previously, the Labor Department reported. The unemployment rate inched down to 9.1 percent from 9.2 percent, partly because some unemployed workers stopped looking for work. Health care providers and manufacturers added jobs.

But the broader fears about the economy are outweighing the improved jobs report and strong corporate earnings, said Dan Greenhaus, chief global strategist at the trading firm BTIG.

“From an economic standpoint, 117,000 jobs is hardly sufficient to boost the economy,” he said. He said it is impossible to tell how long the nervousness will affect the market, but he said it will more likely be years than months.

About twice as many jobs as that must be created every month in order to rapidly reduce the unemployment rate. It has been above 9 percent nearly every month since the recession officially ended in June 2009. Many economists fear that the economy might dip back into recession.

The Dow Jones industrial average plunged 513 points on Thursday. It was the worst day for the Dow since 2008. It is now down 1,500 points, or 11.8 percent, the losing streak began on July 21. The S&P 500 is down 12.5 percent since July 22. All three indexes are in correction. That happens when an index loses more than 10 percent off its recent highs.

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